# zbMATH — the first resource for mathematics

Forward-backward martingale decomposition and compactness results for additive functionals of stationary ergodic Markov processes. (English) Zbl 0936.60037
The author extends forward-backward martingale decomposition of Meyer-Zheng-Lyons’s type from the symmetric case to the general stationary situation for the partial sum $$S.(f)$$ with $$f$$ satisfying a finite energy condition. Furthermore, as corollaries, he obtains a maximal inequality and a tightness result related to the functional central limit and a criterion of a.s. compactness related to the functional law of iterated logarithm.

##### MSC:
 60F17 Functional limit theorems; invariance principles 60J55 Local time and additive functionals
Full Text: